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A223169
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Triangle S(n,k) by rows: coefficients of 3^((n-1)/2)*(x^(1/3)*d/dx)^n when n is odd, and of 3^(n/2)*(x^(2/3)*d/dx)^n when n is even.
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3
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1, 1, 3, 4, 3, 4, 24, 9, 28, 42, 9, 28, 252, 189, 27, 280, 630, 270, 27, 280, 3360, 3780, 1080, 81, 3640, 10920, 7020, 1404, 81, 3640, 54600, 81900, 35100, 5265, 243, 58240, 218400, 187200, 56160, 6480, 243, 58240, 1048320, 1965600
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OFFSET
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0,3
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 3;
4, 3;
4, 24, 9;
28, 42, 9;
28, 252, 189, 27;
280, 630, 270, 27;
280, 3360, 3780, 1080, 81;
3640, 10920, 7020, 1404, 81;
3640, 54600, 81900, 35100, 5265, 243,
58240, 218400, 187200, 56160, 6480, 243
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MAPLE
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a[0]:= f(x):
for i from 1 to 13 do
a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(diff(a[i-1], x$1 )));
end do;
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CROSSREFS
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Cf. A223168-A223172, A223523-A223532, A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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